Date of Award

7-30-2018

Degree Type

Thesis

Degree Name

M.Sc.

Department

Mathematics and Statistics

First Advisor

Severien Nkurunziza

Rights

CC-BY-NC-ND

Abstract

In this thesis, we consider inference problems about the drift parameter vector in generalized mean reverting processes with multiple and unknown change-points. In particular, we study the case where the parameter may satisfy uncertain restrictions. As compared to the results in the literature, we generalize some findings in five ways. First, we consider a statistical model which incorporates uncertain prior information and the uncertain restriction includes as a special case the nonexistence of the change-points. Second, we derive the unrestricted estimator (UE) and the restricted estimator~(RE), and we study their asymptotic properties. Specifically, in the context of a known number of change-points, we derive the joint asymptotic normality of the UE and the RE, under the set of local alternative hypotheses. Third, we derive a test for testing the hypothesized restriction and we derive its asymptotic local power. We also prove that the proposed test is consistent. Fourth, we construct a class of shrinkage type estimators (SEs) which includes as special cases the UE, RE, and classical SEs. Fifth, we derive the relative risk dominance of the proposed estimators. More precisely, we prove that the SEs dominate the UE. The novelty of the derived results consists in the fact that the dimensions of the proposed estimators are random variables. Finally, we present some simulation results which corroborate the established theoretical findings.

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